Zijuan Deng1*
Heather Vice3
Matthew E Gilbert3
Mark A Adams2
Thomas N Buckley3*
1Centre for Carbon, Water and Food, the University of
Sydney; Current: College of Science and Engineering, Flinders
University, Australia
2School of Science, Faculty of Science, Engineering &
Technology, Swinburne University of Technology, Australia
3Department of Plant Sciences, University of
California, Davis, CA, United States
*Corresponding authors:
Zijuan Deng
zijuan.deng@flinders.edu.au/rosedeng0810@gmail.com
*These authors contributed equally to this work.
Abstract
Sap velocity measurements are useful in fields ranging from plant water
relations to hydrology at a range of scales. Heat-pulse based techniques
are among the most common methods to measure sap velocity, but most lack
the ability to measure velocities across a wide range, including very
high, very low and negative velocities (reverse flow). We propose a new
method, the double-ratio method (DRM), which is robust across an
unprecedented range of sap velocities and can provide real-time
estimates of the thermal diffusivity of wood. The DRM employs one
temperature sensor proximal and two distal to the heat pulse probe and
facilitates several theoretical, heat-based approaches to quantifying
sap velocity. We tested the DRM using whole-tree lysimetry inEucalyptus cypellocarpa and found strong agreement across a wide
range of velocities.
Keywords:
Sap flow, sap flux, sap velocity, heat-pulse based technique,Eucalyptus cypellocarpa , thermal diffusivity, double-ratio method
1 Introduction
Sap velocity measurements using heat-tracing techniques have been
important means for studying plant water relations from whole-plant to
catchment scale in the tree
physiology, forestry and hydrology communities (Thomas N. Buckley,
Turnbull, Pfautsch, & Adams, 2011; Thomas N Buckley, Turnbull,
Pfautsch, Gharun, & Adams, 2012; Cermak, Kucera, Bauerle, Phillips, &
Hinckley, 2007; Steppe, Vandegehuchte, Tognetti, & Mencuccini, 2015;
Wilson, Hanson, Mulholland, Baldocchi, & Wullschleger, 2001). There are
many heat-dissipation-based methods, but all have one or more
weaknesses. Constant-power or Granier style probes (Granier, 1985) are
inexpensive and robust but require empirical calibration (Clearwater,
Meinzer, Andrade, Goldstein, & Holbrook, 1999), consume large amounts
of electrical power and cannot accurately measure small or negative sap
velocities. Heat-pulse based methods such as the Tmax method
(Cohen, Fuchs, & Green, 1981),
compensation heat pulse method (CHPM)
(SR Green & Clothier, 1988), heat
field deformation method (HFD) (Nadezhdina, Cermak, & Nadezhdin, 1998),
heat ratio method (HRM) (Burgess et al., 2001), and Sapflow+ method
(Vandegehuchte & Steppe, 2012c) use little power and are traceable to
first principles, but also have critical limitations. Tmax, CHPM and HFD
cannot measure low or negative velocities (Steve Green, Clothier, &
Jardine, 2003; Vandegehuchte & Steppe, 2012c); Sapflow+ suffers from
difficulty in model identification; and the HRM fails at high sap
velocities (Bleby, McElrone, & Burgess, 2008; Flo, Martinez-Vilalta,
Steppe, Schuldt, & Poyatos, 2019; Pearsall, Williams, Castorani, Bleby,
& McElrone, 2014).
In most heat pulse-based methods, sapwood thermal diffusivity, k ,
is a crucial parameter in calculation of the sap velocity (López-Bernal,
Alcántara, & Villalobos, 2014; Vandegehuchte & Steppe, 2012a). An
arbitrary value of k is usually set or obtained from empirical
function related to sapwood moisture content (mc ) (Burgess et
al., 2001; Marshall, 1958; Vandegehuchte & Steppe, 2012a). Howeverk is seemingly not constant, and can change over seasons (Burgess
et al., 2001; Chen, Miller, Rubin, & Baldocchi, 2012) or even diurnally
(López-Bernal et al., 2014), with uncertain consequences for the
accuracy of calculated sap velocity. Velocity estimates from the Tmax
method depend only on k and known parameters. Therefore if sap
velocity is known to be zero, such as at night time after prolonged wet
conditions, k can be directly inferred and then treated as a
constant until such a time that it can be re-measured (Burgess et al.,
2001). Inverse modelling has also been used to calibrate k (Chen
et al., 2012; Vandegehuchte & Steppe, 2012a), notwithstanding
measurement uncertainties and issues with probe alignment. For example,
empirical functions to infer k from sapwood properties andmc could be validated at low sap velocities under 20 cm
h-1 (Vandegehuchte & Steppe, 2012b), however, such
procedures require knowledge of mc , which may vary diurnally
(López-Bernal et al., 2014). k has never been estimated in
vivo , in real time, at higher sap velocities.
Pearsall et al. (2014) proposed a method for extending the range of sap
velocities that can be reliably measured using heat pulse approaches.
They combined the HRM and CHPM, using the HRM to detect small and
negative sap velocities and the CHPM to detect high sap velocities. One
limitation of that approach is the lack of a non-arbitrary method to
selecting whether to use the HRM- or CHPM-derived estimate of sap
velocity at any given time. Another concern is that this approach
alternates between two very different measurement approaches: an average
over time of sap velocity estimated from the ratio of temperature rises
in two sensors (HRM), or an inference based on estimation of the single
instant at which two temperature rises are equal (CHPM). Thus, research
communities that rely on sap velocity measurements lack a single method
that is at once energy-efficient, objective, robust and capable of
measuring negative, low and high sap velocities with a single
measurement principle.
We developed a new and efficient algorithm, the double-ratio method
(DRM), that combines many of the strengths of existing methods and is
robust across an unprecedented range of sap velocities, from moderate
negative velocities to very large positive velocities. The DRM is an
extension of the HRM in which an additional temperature sensor (Probe
#3) is installed distal to both temperature sensors used in the HRM.
The DRM estimates sap velocity based on the same principles as the HRM
– namely, by calculating the ratios of heat pulse-induced temperature
rises measured in different probes. Two different velocity estimates are
produced – one based on Probe #2 and #1 and another based on Probe
#3 and #2 – and the value with the lesser intrinsic uncertainty
(which is calculated based on temperature rises and probe positions) is
retained. Furthermore, the presence of a third sensor also enables CHPM
estimates of flow, which can be combined with DRM-based estimates to
allow real time estimation of k under high-velocity
conditions. We tested the DRM experimentally using weighing
lysimeters and examined its capability by numerical modelling. We
discuss the strengths and weaknesses of the DRM in relation to other
commonly used heat-pulse based techniques.
2 Materials and Methods
2.1 Theory
2.1.1 Background: heat pulse theory and the HRM
Marshall (1958) showed that an instantaneous heat pulse at time t= 0 causes an increase in temperature (δ i) at
both axial (x i) and azimuthal
(y i) positions relative to the heater at timet (s), with negative and positive x ivalues indicating positions proximal and distal to the heater,
respectively: